Meter-wave MIMO radar height measurement method based on sparse array under multipath interference

Abstract

The invention belongs to the technical field of radars, and particularly relates to a meter-wave MIMO radar height measurement method based on a sparse array under multipath interference. Comprising the following steps: S1, constructing an MIMO radar signal model based on a sparse array; and S2, based on the MIMO radar signal model in the step 1, constructing a height measurement method based on a co-occurrence array and a nested array. According to the altitude estimation algorithm based on the sparse array provided by the invention, the influence of multiple paths under simple terrains and complex terrains can be processed at the same time. In a complex terrain, a sparse array is introduced into an MIMO radar system as a transmitting and receiving antenna. A multi-path reflection signal model of the sparse array MIMO radar under the complex terrain is established. A generalized multiple signal classification algorithm and a maximum likelihood algorithm are combined, and a height measurement method suitable for the model is provided. Under a simple terrain, in order to reduce the calculation cost, a real value algorithm and a dimension reduction real value algorithm are provided.

Description

Technical Field

[0001] The invention belongs to the technical field of MIMO radars, and in particular relates to a sparse array-based meter-wave MIMO radar altitude measurement method under multipath interference. Background Art

[0002] Due to the reflected multipath signals, height measurement is a difficult problem in low-elevation areas. This problem can be viewed as how to eliminate coherent signals, and then many corresponding height measurement methods have been developed, such as spatial smoothing technology, reconstruction matrix method [, maximum likelihood estimation, alternating projection technology, compressed sensing, and sparse reconstruction technology. In practical applications, there are multiple reflection paths simultaneously in complex terrain environments. In the past few decades, a large number of studies have been developed to solve such problems. It is worth noting that MIMO radar has shown significant advantages in detecting low-elevation targets with its waveform diversity, and there has been a lot of research work. In addition, there are many complex terrains in actual terrain, such as undulating terrain, inclined terrain, etc. In complex terrain, there is likely to be more than one reflection point, so the accuracy of the above height measurement methods is greatly reduced. In order to solve this problem, a height measurement method based on matrix nesting is studied.

[0003] The above low-angle target positioning algorithms all use uniform linear array MIMO radar signal models, which have the problems of low elevation estimation accuracy and large fluctuations in measurement errors with elevation angle changes. Considering that sparse arrays have larger degrees of freedom and lower mutual coupling, their equivalent aperture is larger than that of uniform linear arrays, so the direction of arrival (DOA) estimation accuracy is better under the same conditions. In addition, for targets with multipath reflections, the phase difference caused by the difference between the direct wave and the reflected wave will be different due to the non-uniformity of the array distance. This makes sparse arrays applicable to elevation estimation. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention takes into account the influence of complex terrain on multipath. First, a practical complex terrain MIMO radar multipath signal model is proposed, which takes into account both transmission multipath and reception multipath. Then, a new altitude estimation technology based on sparse array is proposed. The algorithm can simultaneously deal with the influence of multipath under simple terrain and complex terrain. Under complex terrain, sparse arrays are introduced into the MIMO radar system as transmitting and receiving antennas. A multipath reflection signal model of sparse array MIMO radar under complex terrain is established. Combining the generalized multiple signal classification algorithm and the maximum likelihood algorithm, a height measurement method suitable for the model is proposed. Under simple terrain, in order to reduce the computational cost, a real-valued algorithm and a dimensionality-reduced real-valued algorithm are proposed.

[0005] In order to achieve the above technical effects and the above objectives, the present invention provides a sparse array-based meter-wave MIMO radar altitude measurement method under multipath interference, comprising:

[0006] S1: Construct a MIMO radar signal model based on sparse array;

[0007] S2: Based on the MIMO radar signal model in step 1, a height measurement method based on symbiotic arrays and nested arrays is constructed to achieve height measurement of the radar to the target.

[0008] Preferably, S1 comprises:

[0009] S1.1: Construct the multipath signal model x(t) of MIMO radar under complex multipath:

[0010]

[0011] Among them, j is an imaginary number, δ i =2πΔR i / λ, wavelength λ, s(t)=[s1(t),....,s M (t)] T is the transmission signal vector of the MIMO radar, e is the exponential with natural numbers as the base, I represents the reflection point, and ρ si is the reflection coefficient at the reflection point, For the basic received signal without interference, θ d is the elevation angle of the sparse array sensor;

[0012] Among them, a(θ d ),a(θ s,i ) are the steering vectors of the directed wave and the reflected wave, respectively, expressed as:

[0013]

[0014] Where, d=[d1,....,d M ] T is the location of the sparse array sensor;

[0015] S1.2: According to the reciprocity theorem, the multipath effect needs to be added to the receiving array. The principle is the same as the transmission multipath effect. Therefore, the expression of the data received by the receiver is obtained:

[0016]

[0017] Among them, β(t) represents the target scattered echo, n(t) represents the mean and variance Gaussian white noise that is all zero;

[0018] S1.3: Match filtering the formula of S1.2 to obtain:

[0019]

[0020] δ i is the reflection coefficient of the i-th target;

[0021] S1.4: Vectorize X(t) of S1.3:

[0022]

[0023] The vec function defines a vectorized operation, which is to arrange the matrix in a column-by-column manner.

[0024] Preferably, the height measurement method based on the symbiotic array and the nested array constructed by S2 comprises:

[0025] S2.1: Construct a basic algorithm based on the generalized MUSIC algorithm and the ML algorithm to realize the low-altitude target height measurement of meter-wave MIMO radar based on sparse array;

[0026] S2.2: Construct a real-value processing algorithm to achieve low-altitude target height measurement using sparse array-based meter-wave MIMO radar;

[0027] S2.3: Based on S2.1 and S2.2, a dimensionality reduction real-value processing algorithm is constructed to realize the low-altitude target height measurement of meter-wave MIMO radar based on sparse array.

[0028] Preferably, S2.1 includes:

[0029] S2.1.1: Assuming the number of reflection points is 2, simplify equation S1.3 to obtain:

[0030]

[0031] A(θ d ,θ s,1 ,θ s,2 ) is the steering vector of the received data, a(θ d ),a(θ s,1 ),a(θ s,2 ) is a sparse array steering vector;

[0032] The position of the nested array sensor and the steering vector a(θ d ),a(θ s,1 ),a(θ s,2 ) are:

[0033] d=[d1,d2,d3,d4,d5,d6] T

[0034] =[1d,2d,3d,4d,8d,12d]T

[0035]

[0036]

[0037] S2.1.2: θ s,2 ,θ s,1 and θ d The geometric relationship is:

[0038] θ s,i ≈(arctan(tanθ d +2h a / R)+θ q,i )

[0039] Among them, h a is the reference element height, θ q,i is the ground inclination angle at the reflection point, θ s,i is the direction of the reflected wave at the reflection point, R is the distance from the radar projection point to the horizontal ground and the target projection point;

[0040] S2.1.3: If the steering vector matches the terrain, the inclination angle can be obtained in advance through terrain reconnaissance, so A(θ d ,θ s,1 ,θ s,2 ) is written as A(θ d ), and A(θ d ) is denoted as A(θ);

[0041] S2.1.4: According to the maximum likelihood estimation criterion, the received data covariance matrix is ​​obtained from the following equation:

[0042]

[0043] Where L represents the number of snapshots, and the noise subspace E n The peak search formula of the generalized MUSIC algorithm is obtained by eigenvalue decomposition of the covariance matrix:

[0044]

[0045] S2.1.5: The steering vector matrix constructs the spatial projection matrix of the ML algorithm as follows:

[0046] P a (θ) = A(θ)(A H (θ)A(θ)) -1 A H (θ)

[0047] S2.1.6: The peak search formula of the ML algorithm is:

[0048]

[0049] S2.1.7: The elevation angle θ of the target is obtained by using the spectrum peak search formula of the generalized MUSIC algorithm in S2.1.4 and the spectrum peak search formula of the ML algorithm in S2.1.6. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the radar's measured height of the target.

[0050] Preferably, S2.2.1: Spectral peak search formula of real-valued MUSIC algorithm:

[0051]

[0052] Where U n is the real-valued noise subspace obtained by eigenvalue decomposition of the real-valued covariance matrix, A U (θ) is the real-valued composite steering vector;

[0053] S2.2.2: The peak search formula of the UML algorithm is as follows:

[0054]

[0055] in, I p : The identity matrix of dimension P;

[0056] S2.2.3: The elevation angle θ of the target is obtained by using the spectrum peak search formula of the real-valued MUSIC algorithm in S2.2.1 and the spectrum peak search formula of the UML algorithm in S2.2.2. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the height of the target.

[0057] Preferably, S2.3.1: the spectrum peak search formula of the dimensionality reduction real value algorithm is expressed as follows:

[0058]

[0059] A URD (θ) is the dimension-reduced real-valued steering vector, Eigenvalue decomposition is the dimension reduction of the real-valued received data covariance matrix

[0060] S2.3.2: The RD-UML peak search formula for the dimensionality reduction real-valued algorithm is:

[0061]

[0062] in, The dimension is the identity matrix of PRD, trace: find the trace operation of the matrix;

[0063] S2.3.3: Through the spectrum peak search formula of the dimensionality reduction real value algorithm in S2.3.1 and the RD-UML spectrum peak search formula in S2.3.2, the elevation angle θ of the target is obtained. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the height of the target.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] The present invention firstly proposes a practical complex terrain MIMO radar multipath signal model, taking into account both transmission multipath and reception multipath. Then a new altitude estimation technology based on sparse array is proposed. The algorithm can simultaneously deal with the influence of multipath under simple terrain and complex terrain. Under complex terrain, sparse arrays are introduced into the MIMO radar system as transmitting and receiving antennas. A multipath reflection signal model of sparse array MIMO radar under complex terrain is established. Combining the generalized multiple signal classification algorithm and the maximum likelihood algorithm, a height measurement method suitable for the model is proposed. Under simple terrain, in order to reduce the computational cost, a real-valued algorithm and a dimensionality-reduced real-valued algorithm are proposed.

[0066] Through simulation experiments, it is found that the RMSE of all algorithms decreases with the increase of signal-to-noise ratio, which is consistent with the theoretical analysis results. Compared with GMUSIC based on ULA, the RMSE of angle and height estimation based on array and nested array is much smaller, indicating that the three GMUSIC algorithms based on array and nested array are effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0068] In the attached picture:

[0069] Figure 1 This is a diagram of the symbiotic array structure.

[0070] Figure 2 This is a two-level nested array structure diagram.

[0071] Figure 3 It is the terrain multipath reflection model.

[0072] Figure 4 Comparison of RMSE and signal-to-noise ratio under simple terrain: Figure 4 (a) is the RMSE of angle estimation; Figure 4 (b) RMSE of height estimation.

[0073] Figure 5 This is the comparison between RMSE and the signal-to-noise ratio of different algorithms under simple terrain.

[0074] Figure 6 Comparison of RMSE and signal-to-noise ratio under complex terrain: Figure 6 (a) is the RMSE of angle estimation; Figure 6 (b) RMSE of height estimation.

[0075] Figure 7 This is the comparison between RMSE and the signal-to-noise ratio of different algorithms under complex terrain.

[0076] Figure 8 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0077] The following is combined with Figure 1-8 The preferred embodiments of the present invention are described. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0078] S1: Construct a MIMO radar signal model based on sparse array;

[0079] S1.1: Construct the multipath signal model x(t) of MIMO radar under complex multipath:

[0080] Signal Model

[0081] Consider a vertically placed sparse array radar using a coexistence array or a nested array as the transmit and receive antennas. The structure of the coexistence array is as follows: Figure 1 As shown, the structure of the nested array is as follows Figure 2 As shown. The symbiotic array consists of two sparse uniform sub-arrays, that is, the number of elements is M and N (M<N), the spacing of the elements is Nd and Md, M and N are a pair of symbiotic integers, and d is half the wavelength. By linearly superposing and combining two sparse uniform sub-arrays in the form of first element overlap, a symbiotic array containing the number of physical elements is obtained, and the position of the end element is. The nested array consists of two uniform linear arrays, the total number of array elements is N=N1+N2, and the first-level sub-array has N1 elements with d spacing. Considering that the height measurement scenario is based on the multipath reflection model of sparse arrays under complex terrain. Figure 3 is the terrain multipath reflection model, where the array antenna is a sparse array, h a is the reference element height (set to the lowest element height), h t is the target height, θ q,i is the ground inclination angle at the reflection point, θ s,i is the direction of the reflected wave at the reflection point, and B and C represent the reflection points of the two reflection paths.

[0082] Assume that the signal emitted by the MIMO radar sensor at time t is:

[0083]

[0084] Where f0 is the carrier frequency, φ m is the initial phase. For convenience and without loss of generality, φ m Set to zero, s m (t) indicates that the sensor is in a state of duration T p The complex envelope of the transmission signal of seconds has unit energy. The transmission signal of the sensor hitting the target can be expressed as:

[0085]

[0086] Among them, τ d,m =R d,m / c is the direct path time delay of the sensor, R d,m is the distance of the sensor in the direct path. According to the geometric relationship, R d,m It is expressed as:

[0087]

[0088] In the formula, h m is the height of the sensor, R is the distance from the radar projection point to the horizontal ground and the target projection point, R r is the horizontal distance between the radar and the target;

[0089] Based on the fact that the transmitted signal is reflected by the I reflection point and reaches the target, the sensor signal reaching the target after reflection is:

[0090]

[0091] Among them, ρ si is the reflection coefficient of the reflection point. The wavelength of meter-wave radar is relatively long, and the detection targets are mostly far-field targets, which can easily meet the Rayleigh condition: h sinθ d <λ / 8. Here we use horizontal polarization wave, ρ si It is expressed as follows:

[0092] ρ s,i =ρ i ρ D ζ i (5)

[0093]

[0094]

[0095] In the formula, ρ i is the Fresnel reflection coefficient of the reflection point, and its value is related to the ground emitting medium, ρ D is the divergence coefficient, RE is the radius of the earth, r1 is the distance between the radar projection to the ground and the reflection point, r2 is the distance between the reflection point and the vertical projection of the target. In low altitude areas, the divergence factor is 1, which is the surface roughness factor of the reflection point, and its value is related to the scraping angle ψ of the reflection point. i , ground fluctuation variance σ h Related to wavelength λ, τ si,m =R si,m / c is the time difference between the reflected wave at the reflection point and the sensor, R si,m is the distance of the reflected wave, and its expression is:

[0096]

[0097] Among them, h s,i is the height of the reflection point.

[0098] Therefore, under complex multipath conditions, the transmission signal of the sensor hitting the target can be expressed as:

[0099]

[0100] The transmitted signal of MIMO radar is a narrowband signal, so the time shift will not affect the complex envelope of the signal, that is:

[0101] s m (t-τ d,m )≈s m (t-τ si,m )=s m (t)(11)

[0102] Using (11) in (10) yields:

[0103]

[0104] ΔR i is the distance difference between the direct wave and the reflected wave, which can be expanded using the binomial theorem. si,m and R d,m (Because R>>h t and R>>h n , only considering the first two terms), the distance difference between the direct wave and the reflected wave is expressed as

[0105]

[0106] Substituting equation (13) and λ = c / f into equation (12), we obtain:

[0107]

[0108] in, Therefore, the multipath signal model x(t) of MIMO radar under complex multipath is constructed:

[0109]

[0110] Among them, j is an imaginary number, δ i =2πΔR i / λ, wavelength λ, s(t)=[s1(t),....,s M (t)] T is the transmission signal vector of the MIMO radar, e is the exponential with natural numbers as the base, I represents the reflection point, and ρ si is the reflection coefficient at the reflection point, For the basic received signal without interference, θ d is the elevation angle of the sparse array sensor;

[0111] Among them, δ i =2πΔR i / λ、s(t)=[s1(t),....,s M (t)] T is the transmission signal vector of the MIMO radar, a(θ d ),a(θ s,i ) are the steering vectors of the directed wave and the reflected wave, respectively, expressed as:

[0112]

[0113] Where, d=[d1,....,d M ] T is the location of the sparse array sensor;

[0114] S1.2: According to the reciprocity theorem, the multipath effect should also be considered for the receiving array. The principle is the same as the transmission multipath effect. Therefore, the expression of the data received by the receiver is obtained:

[0115]

[0116] Among them, β(t) represents the target scattered echo, n(t) represents the mean and variance Gaussian white noise that is all zero;

[0117] Where n(t) is the mean and variance Gaussian white noise that is all zero;

[0118] S1.3: Matching filter on formula (17) yields:

[0119]

[0120] δ i is the reflection coefficient of the i-th target;

[0121] S1.4: Vectorize X(t) of S1.3:

[0122]

[0123] The vec function defines a vectorized operation, which is to arrange the matrix in a column-by-column manner.

[0124] S2 constructed a height measurement method based on symbiotic arrays and nested arrays:

[0125] The difference between the MIMO radar signal model and the traditional array radar signal model lies mainly in the relationship between the direct wave and the reflected wave. In the traditional array radar, the direct wave and the reflected wave can be equivalent to the coherent signal. In the MIMO radar, especially the sparse array used in the transceiver antenna, the traditional decoherence algorithms such as spatial smoothing and matrix reconstruction are not suitable. Therefore, the generalized MUSIC or maximum likelihood estimation algorithm is studied to obtain low elevation angles, and the following three GMUSIC-based meter-wave MIMO radar height measurement algorithms are proposed: basic algorithm, real value processing algorithm and dimensionality reduction real value processing algorithm.

[0126] S2.1: Construct a basic algorithm based on the generalized MUSIC algorithm and the ML algorithm to realize the low-altitude target height measurement of meter-wave MIMO radar based on sparse array;

[0127] The traditional MUSIC algorithm uses the orthogonality of the signal space and the noise space to search for spectrum peaks. Inspired by the traditional MUSIC algorithm, the MUSIC algorithm and the ML algorithm are proposed to match complex terrain. In addition, the low-altitude target height measurement method of meter-wave MIMO radar based on sparse array is also studied to improve the accuracy of low elevation angles in complex terrain.

[0128] S2.1.1: For ease of analysis, we assume that the number of reflection points is 2 and simplify equation (19) to obtain:

[0129]

[0130] A(θ d ,θ s,1 ,θ s,2 ) is the steering vector of the received data, a(θ d ),a(θ s,1 ),a(θ s,2 ) is the sparse array steering vector; for example, if a two-level nested array is used, the first-level sub-array has 4 elements, the second-level sub-array has 3 elements, and the two sub-arrays share the first element, then the total number of nested arrays is 6, and the position and steering vector a(θ of the nested array sensor is d ),a(θs,1 ),a(θ s,2 ) are:

[0131]

[0132] Among them, A(θ d ,θ s，1 ,θ s，2 ) three unknown parameters.

[0133] S2.1.2: θ s,2 ,θ s,1 and θ d The geometric relationship is:

[0134] θ s,i ≈(arctan(tanθ d +2h a / R)+θ q,i )(27)

[0135] Among them, h a is the reference element height, θ q,i is the ground inclination angle at the reflection point, θ s,i is the direction of the reflected wave at the reflection point, R is the distance from the radar projection point to the horizontal ground and the target projection point;

[0136] S2.1.3: If the steering vector matches the terrain, the inclination angle can be obtained in advance through terrain reconnaissance, so A(θ d ,θ s,1 ,θ s,2 ) can be written as A(θ d ), and A(θ d ) can be denoted as A(θ);

[0137] S2.1.4: According to the maximum likelihood estimation criterion, the received data covariance matrix can be obtained from the following equation:

[0138]

[0139] Where L represents the number of snapshots, and the noise subspace E n It is obtained by eigenvalue decomposition of the covariance matrix. Different from the steering vector in the traditional MUSIC algorithm, this steering vector is orthogonal to the noise subspace. Therefore, the spectrum peak search formula of the generalized MUSIC algorithm is:

[0140]

[0141] S2.1.5: Accordingly, the spatial projection matrix of the ML algorithm is constructed using the steering vector matrix proposed in this paper as follows:

[0142] Pa (θ) = A(θ)(A H (θ)A(θ)) -1 A H (θ) (30)

[0143] S2.1.6: Therefore, the peak search formula of the ML algorithm is:

[0144]

[0145] S2.1.7: The elevation angle θ of the target is obtained through the spectrum peak search formula of the generalized MUSIC algorithm in S2.1.4 and the spectrum peak search formula of the ML algorithm in S2.1.6. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the measured height of the radar to the target.

[0146] S2.2: Construct a real-value processing algorithm to achieve low-altitude target height measurement using sparse array-based meter-wave MIMO radar;

[0147] MIMO radar greatly increases the amount of calculation while improving system performance. In order to reduce the complexity of the algorithm and further improve its accuracy, we continue to study a real-valued height measurement method. The known unitary matrix can be transformed from the central-Hermitian matrix to a real matrix through unitary transformation. The received data covariance matrix is not a centered Hermitian matrix, then the centered Hermitian matrix is The true value covariance matrix is ​​obtained by forward and backward spatial smoothing. By unitary transformation we get:

[0148]

[0149] The definition of U matrix is ​​as follows:

[0150]

[0151] If N is an even number, and K = N / 2, or

[0152]

[0153] If N is an odd number and K = (N-1) / 2, I K and Π K The definition is as follows:

[0154]

[0155] S2.2.1: Similar to formula (29), the following formula is obtained:

[0156]

[0157] Where U n is the real-valued noise subspace obtained by eigenvalue decomposition of the real-valued covariance matrix, A U (θ) is the real-valued composite steering vector;

[0158] A U (θ)=U H A(θ) (39)

[0159] S2.2.2: Similarly, the search spectrum of the UML algorithm is as follows:

[0160]

[0161] in,

[0162] S2.2.3: The elevation angle θ of the target is obtained by using the spectrum peak search formula of the real-valued MUSIC algorithm in S2.2.1 and the spectrum peak search formula of the UML algorithm in S2.2.2. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the height of the target.

[0163] S2.3: Based on S2.1 and S2.2, a dimensionality reduction real-value processing algorithm is constructed to realize the low-altitude target height measurement of meter-wave MIMO radar based on sparse array.

[0164] Although the real-valued processing algorithm reduces the computational complexity, it is only one order of magnitude lower than the basic algorithm. In order to further reduce the computational complexity of the algorithm, a dimensionality reduction real-valued processing algorithm is proposed.

[0165] From the expression of the steering vector, we can get:

[0166]

[0167] Where a(θ)=[a(θ d )a(θ s,1 )a(θ s,2 )];

[0168] is the imaginary linear array steering vector, and

[0169]

[0170] Substituting formula (41) into formula (20), we obtain:

[0171]

[0172] It can be seen from formula (43) that the received data matrix is ​​a high-dimensional space spanned by the virtual array steering vector d(θ), which can be converted into a low-dimensional space through dimensionality reduction processing. Let the dimensionality reduction matrix (2M-1)*M 2 is the Q matrix, then the received data matrix is:

[0173]

[0174] Among them, N RD =Q*vec(N(t)).

[0175] Assume that the noise vector after dimensionality reduction should be Gaussian white noise, and Q satisfies the relationship: QQ H =I 2M-1 , and the dimension reduction matrix can be expressed as:

[0176] Q=(D H D) -1 / 2 D H (45)

[0177] Q=(D H D) -1 / 2 D H Substituting into (43), we obtain:

[0178]

[0179] Define T = D H D and T = diag(1,2,…,M,…2,1), where diag(·) represents a diagonal matrix, and then the covariance matrix processing is performed on the data received after the dimensionality reduction processing:

[0180]

[0181] After dimensionality reduction, the dimension of the covariance matrix of the received data becomes (2M-1)*(2M-1), that is, the dimension is greatly reduced. The reduced-dimensional matrix is ​​sparse, and the increase in calculation is not obvious.

[0182] After dimensionality reduction, the covariance matrix of the received data is as follows:

[0183]

[0184] The data received is the covariance matrix It is still complex, and its computational complexity can be further reduced by real-value processing. RD-UGMUSIC and RD-UML are used to mark the dimensionality reduction real-valued GMUSIC algorithm and the dimensionality reduction real-valued ML algorithm.

[0185] S2.3.1: The spectrum peak search formula of the dimensionality reduction real-valued algorithm is expressed as follows:

[0186]

[0187] A URD (θ) is the dimension-reduced real-valued steering vector, Eigenvalue decomposition is the dimension reduction of the real-valued received data covariance matrix A URD (θ d ,θ s,1 ,θ s,2 )and The expression is as follows:

[0188] A URD (θ d ,θ s,1 ,θ s,2 )=UQA(θ d ,θ s,1 ,θ s,2 ) (50)

[0189]

[0190] S2.3.2: Similarly, the RD-UML peak search formula for the dimensionality reduction real-valued algorithm is:

[0191]

[0192] in, The dimension is the identity matrix of PRD, trace: find the trace operation of the matrix;

[0193] S2.3.3: Through the spectrum peak search formula of the dimensionality reduction real value algorithm in S2.3.1 and the RD-UML spectrum peak search formula in S2.3.2, the elevation angle θ of the target is obtained. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the height of the target.

[0194] The steps of the MIMO radar altitude measurement method based on sparse arrays in complex terrain are summarized as follows:

[0195] Step 1: Calculate the direct wave a(θ d ) and the reflected wave a(θ s,i )’s steering vector;

[0196] Step 2: Calculate the covariance matrix and noise subspace;

[0197] In the basic algorithm, the covariance matrix From equation (27), we get the subspace E n The covariance matrix can be The eigenvalue decomposition of is obtained;

[0198] In the real-valued processing algorithm, the real-valued covariance matrix is ​​obtained from equation (32): By the real-valued covariance matrix The noise subspace U is obtained by eigenvalue decomposition n ;

[0199] In the dimensionality reduction real value processing algorithm, the dimensionality reduction real value covariance matrix is ​​obtained by formula (48): By the real-valued covariance matrix The noise subspace U is obtained by eigenvalue decomposition RDn ;

[0200] Step 3: Calculate the composite steering vector;

[0201] In the basic algorithm, the composite steering vector A(θ) is obtained by equation (21);

[0202] In the real-value processing algorithm, the real-valued composite steering vector A can be obtained through formula (36): U (θ);

[0203] In the dimensionality reduction real value processing algorithm, the dimensionality reduction real value composite steering vector A can be obtained through formula (47): URD (θ);

[0204] Step 4: Calculate the target's elevation angle:

[0205] In the basic algorithm, the elevation angle of the target is calculated by equations (29) and (31);

[0206] In the real-value algorithm, the elevation angle of the target is calculated by equations (38) and (40);

[0207] In the dimension reduction real value algorithm, the elevation angle of the target is calculated by equations (49) and (52);

[0208] Step 5: The height of the target is calculated by the target height according to the geometric relationship of the target:

[0209] In the basic algorithm, the obtained elevation angle θ is substituted into the geometric relationship formula of S2.1.2 to obtain the height of the target.

[0210] In the real-value algorithm, the obtained elevation angle θ is substituted into the geometric relationship formula of S2.1.2 to obtain the height of the target.

[0211] In the dimensionality reduction real value algorithm, the obtained elevation angle θ is substituted into the geometric relationship formula of S2.1.2 to obtain the height of the target.

[0212] Complexity Analysis

[0213] The complexity of the algorithm is analyzed. First, the complexity of the three algorithms mainly includes three parts: the construction of the covariance matrix of the received data, the eigenvalue decomposition of the covariance matrix, and the search for spectrum peaks. In addition, the real-value processing algorithm and the dimensionality reduction real-value processing algorithm also involve the complexity of real-value processing and dimensionality reduction real-value processing. In the real-value processing algorithm, the real-value composite steering vector A is calculated. U (θ) and the real-valued covariance matrix In the dimension reduction real value processing algorithm, the dimension reduction real value composite steering vector A is further calculated. URD (θ) and the reduced-dimensional real-valued covariance matrix Considering that both the unitary matrix and the reduced-dimensional matrix are sparse, the complexity of real-valued processing and reduced-dimensional real-valued processing is very small. So it is ignored. Secondly, it is well known that the computational complexity of addition operation is much smaller than that of multiplication. Thirdly, complex-valued multiplication is four times that of real-valued multiplication. In summary, the complexity of these three algorithms is shown below.

[0214] Complexity of basic GMUSIC and ML algorithms in C GMUSIC and C ML The complexity of real-valued GMUSIC and ML algorithms is expressed in C UGMUSIC and C UML The complexity of the dimensionality reduction real-valued GMUSIC and ML algorithms is expressed in C RD-UGMUSIC and C RD-UML express.

[0215] C GMUSIC =4M 4 L+4M 6 +4θ(8M 2 +2M 4 ) (53)

[0216] C ML =4M 4 (L+M 2 )+4θ(8M 2 +2M 4 +M 6 )(54)

[0217] C UGMUSIC =M 4 L+M 6 +Θ(8M 2 +2M 4 ) (55)

[0218] C UML =M 4 (L+M 2 )+Θ(8M 2 +2M 4 +M 6 ) (56)

[0219]

[0220] simulation

[0221] Several simulation methods are proposed to evaluate the performance of the proposed method. It is compared with the uniform linear array based GMUSIC, UGMUSIC and RD-UGMUSIC algorithms. The uniform linear array based GMUSIC, UGMUSIC and RD-UGMUSIC algorithms are marked as ULA-GMUSICULA-UGMUSIC and ULA-RD-UGMUSIC in all figures.

[0222] The GMUSIC, UGMUSIC, and RD-UGMUSIC algorithms based on nested arrays are labeled NA-GMUSIC, NA-UGMUSIC, and NA-RD-UGMUSIC in all figures. The GMUSIC, UGMUSIC, and RD-UGMUSIC algorithms based on co-occurrence arrays are labeled CPA-GMUSIC, CPA-UGMUSIC, and CPA-RD-UGMUSIC, respectively.

[0223] In all the following simulations, RMSE is defined as:

[0224]

[0225] Where RMSE_DOA is the angle estimate of RMSE, and RMSE_H is the height measurement of RMSE. is the target number. P is the number of Monte Carlo tests. K is the estimated value of the target elevation in the experiment. is the target elevation angle; is the estimated value of the target height in the experiment, H p is the target height.

[0226] Example 1: The first simulation considers a scenario with only one reflection path. Therefore, the number of receive paths is 2 in total. Assume that the number of transmitting array elements M = 5, i.e. the number of receiving array elements N = 5. The radar operates at f = 300 MHz. The transmitting and receiving sensor locations of the co-frequency array are d t =[5d,10d,15d,20d,25d] and d r =[0,6d,12d,18d,24d], the transmitting and receiving sensor positions of the nested array are d t =[0,d,2d,3d,4d] and d r =[5d,11d,16d,23d,29d]. This gives the following direct angle θ d =3° indirect angle θs1 =-3°.

[0227] Figure 4 The RMSE of angle and height estimation and signal-to-noise ratio are shown. This experiment mainly verifies the performance changes of three GMUSIC height measurement methods based on co-occurring arrays and nested arrays, as well as the changes in signal-to-noise ratio in the range of [-10dB, 10dB]. It can be seen that the RMSE of all algorithms decreases with the increase of signal-to-noise ratio, which is consistent with the results of theoretical analysis. Compared with GMUSIC based on ULA, the RMSE of angle and height estimation based on array and nested array is much smaller, indicating that the three GMUSIC algorithms based on array and nested array are effective.

[0228] In addition, it is not difficult to find that the three GMUSIC height measurement algorithms have their advantages and disadvantages. Compared with the GMUSIC algorithm, the real-valued GMUSIC algorithm and the reduced-dimensional real-valued GMUSIC algorithm have poorer estimation accuracy, but in the case of the same array structure, the computational complexity is lower. Figure 5 The RMSE and signal-to-noise ratio of different algorithms are shown. Figure 5 It can be seen that the ULA-DBF algorithm outperforms the ULA-GMUSIC algorithm and the ULA-MDL algorithm in terms of estimation accuracy. More importantly, the performance of the proposed NA-GMUSIC algorithm is equivalent to that of ULA-DBF.

[0229] Example 2: The second simulation considers a scenario with two reflection paths. Therefore, the number of receive paths is 3 in total. Assume that the number of transmitting array elements M = 10, i.e. the number of receiving array elements N = 10. The operating frequency of the radar is f = 300 MHz. The transmitting and receiving sensor positions of the co-frequency array are d = [0, 5d, 6d, 10d, 12d, 15d, 18d, 20d, 24d, 25d] and the transmitting and receiving sensor positions of the nested array are d = [0, d, 2d, 3d, 4d, 5d, 11d, 16d, 23d, 29d], which gives the following direct angle θ d =3°, indirect angle θ s1 =-5°,θ s2 =-6°.

[0230] Figure 6The RMSE of angle and height estimation and signal-to-noise ratio are shown. This experiment mainly verifies the performance changes of height measurement methods based on different arrays and the changes of signal-to-noise ratio in the range of [-10dB, 10dB]. It can be seen that the RMSE of all algorithms decreases with the increase of signal-to-noise ratio, which is consistent with the theoretical analysis results. Compared with GMUSIC based on ULA, the RMSE of angle and height estimation based on array and nested array is much smaller, indicating that the three GMUSIC algorithms based on array and nested array are effective. Figure 7 The RMSE and signal-to-noise ratio of different algorithms are shown. Figure 7 It can be seen that the CPA-GMUSIC algorithm is better than other algorithms.

[0231] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A sparse array based meter-wave MIMO radar height measurement method under multipath interference, characterized in that: include: S1: Construct a MIMO radar signal model based on sparse array; S2: Based on the MIMO radar signal model in step 1, a height measurement method based on symbiotic arrays and nested arrays is constructed to achieve height measurement of the radar to the target.

2. The method for measuring the height of a meter-wave MIMO radar based on a sparse array under multipath interference according to claim 1, characterized in that: S1 includes: S1.1: Construct the multipath signal model x(t) of MIMO radar under complex multipath: Among them, j is an imaginary number, δ i =2πΔR i / λ, wavelength λ, s(t)=[s1(t),....,s M (t)] T is the transmission signal vector of the MIMO radar, e is the exponential with natural numbers as the base, I represents the reflection point, and ρ si is the reflection coefficient at the reflection point, For the basic received signal without interference, θ d is the elevation angle of the sparse array sensor; Among them, a(θ d ),a(θ s,i ) are the steering vectors of the directed wave and the reflected wave, respectively, expressed as: Where, d=[d1,....,d M ] T is the location of the sparse array sensor; S1.2: According to the reciprocity theorem, the multipath effect needs to be added to the receiving array. The principle is the same as the transmission multipath effect. Therefore, the expression of the data received by the receiver is obtained: Among them, β(t) represents the target scattered echo, n(t) represents the mean and variance Gaussian white noise that is all zero; S1.3: Match filtering the formula of S1.2 to obtain: δ i is the reflection coefficient of the i-th target; S1.4: Vectorize X(t) of S1.3: The vec function defines a vectorized operation, which is to arrange the matrix in a column-by-column manner.

3. The method for measuring the height of a meter-wave MIMO radar based on a sparse array under multipath interference according to claim 2, characterized in that: S2 constructed height measurement methods based on symbiotic arrays and nested arrays including: S2.1: Construct a basic algorithm based on the generalized MUSIC algorithm and the ML algorithm to realize the low-altitude target height measurement of meter-wave MIMO radar based on sparse array; S2.2: Construct a real-value processing algorithm to achieve low-altitude target height measurement using sparse array-based meter-wave MIMO radar; S2.3: Based on S2.1 and S2.2, a dimensionality reduction real-value processing algorithm is constructed to realize the low-altitude target height measurement of meter-wave MIMO radar based on sparse array.

4. The method for measuring the height of a meter-wave MIMO radar based on a sparse array under multipath interference according to claim 3, characterized in that: S2.1 includes: S2.1.1: Assuming the number of reflection points is 2, simplify equation S1.3 to obtain: A(θ d ,θ s,1 ,θ s,2 ) is the steering vector of the received data, a(θ d ),a(θ s,1 ),a(θ s,2 ) is a sparse array steering vector; The position of the nested array sensor and the steering vector a(θ d ),a(θ s,1 ),a(θ s,2 ) are: d=[d1,d2,d3,d4,d5,d6] T <h2 style=";text-align:left;direction:ltr">(1d, 2d, 3d, 4d, 8d, 12d)<h2 style=";text-align:left;direction:ltr"> T S2.1.2: θ s,2 ,θ s,1 and θ d The geometric relationship is: θ s,i ≈(arctan(tanθ d +2h a / R)+θ q,i ) Among them, h a is the reference element height, θ q,i is the ground inclination angle at the reflection point, θ s,i is the direction of the reflected wave at the reflection point, R is the distance from the radar projection point to the horizontal ground and the target projection point; S2.1.3: If the steering vector matches the terrain, the inclination angle can be obtained in advance through terrain reconnaissance, so A(θ d ,θ s,1 ,θ s,2 ) is written as A(θ d ), and A(θ d ) is denoted as A(θ); S2.1.4: According to the maximum likelihood estimation criterion, the received data covariance matrix is ​​obtained from the following equation: Where L represents the number of snapshots, and the noise subspace E n The peak search formula of the generalized MUSIC algorithm is obtained by eigenvalue decomposition of the covariance matrix: S2.1.5: The steering vector matrix constructs the spatial projection matrix of the ML algorithm as follows: P a (θ)=A(θ)(A H (θ)A(θ)) -1 A H (i) S2.1.6: The peak search formula of the ML algorithm is: S2.1.7: The elevation angle θ of the target is obtained by using the spectrum peak search formula of the generalized MUSIC algorithm in S2.1.4 and the spectrum peak search formula of the ML algorithm in S2.1.

6. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the radar's measured height of the target.

5. The method for measuring the height of a meter-wave MIMO radar based on a sparse array under multipath interference according to claim 4, characterized in that: S2.2.1: Spectral peak search formula of real-valued MUSIC algorithm: Where U n is the real-valued noise subspace obtained by eigenvalue decomposition of the real-valued covariance matrix, A U (θ) is the real-valued composite steering vector; S2.2.2: The peak search formula of the UML algorithm is as follows: in, I p : The identity matrix of dimension P; S2.2.3: The elevation angle θ of the target is obtained by using the spectrum peak search formula of the real-valued MUSIC algorithm in S2.2.1 and the spectrum peak search formula of the UML algorithm in S2.2.

2. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the height of the target.

6. The method for measuring the height of a meter-wave MIMO radar based on a sparse array under multipath interference according to claim 5, characterized in that: S2.3.1: The spectrum peak search formula of the dimensionality reduction real-valued algorithm is expressed as follows: A URD (θ) is the reduced-dimensional real-valued steering vector, U RDn Eigenvalue decomposition is the dimension reduction of the real-valued received data covariance matrix S2.3.2: The RD-UML peak search formula for the dimensionality reduction real-valued algorithm is: in, The dimension is the identity matrix of PRD, trace: find the trace operation of the matrix; S2.3.3: Through the spectrum peak search formula of the dimensionality reduction real value algorithm in S2.3.1 and the RD-UML spectrum peak search formula in S2.3.2, the elevation angle θ of the target is obtained. Then, the elevation angle θ is substituted into the geometric relationship formula in S2.1.2 to obtain the height of the target.

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